For the cubic function $f(x) = x^3 - 3x + a$, the function $$F(x) = \int_{0}^{x} f(t)\, dt$$ has exactly one extremum. What is the minimum value of the positive number $a$? [4 points] (1) 1 (2) 2 (3) 3 (4) 4 (5) 5
For the cubic function $f(x) = x^3 - 3x + a$, the function
$$F(x) = \int_{0}^{x} f(t)\, dt$$
has exactly one extremum. What is the minimum value of the positive number $a$? [4 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5